Operations with Polynomials: Adding, Subtracting, Multiplying, and Dividing

This video tutorial covers operations with polynomials, including addition, subtraction, multiplication, and division. It explains how to add polynomials by combining like terms, subtract by distributing negatives, and multiply using methods like FOIL and the box method. The tutorial also delves into polynomial long division and synthetic division, providing step-by-step examples for each operation.

What is the result of adding the polynomials 5x^2 + 7x + 4 and 3x^2 - 3x - 6?

• 2x^2 + 4x - 2

• 8x^2 + 10x - 2

• 8x^2 + 4x + 2

• 8x^2 + 4x - 2

When subtracting polynomials, what is a common mistake students make?

• Not combining like terms

• Forgetting to distribute the negative sign to all terms

• Combining constants incorrectly

• Starting with the lowest exponent

What is the result of subtracting the polynomials x^2 + 7x + 9 and 3x^2 - 2x - 6?

• 4x^2 + 5x + 15

• 4x^2 + 9x - 3

• 2x^2 + 9x + 3

• 4x^2 + 9x + 3

Which method is used to multiply the binomials 3x + 2 and 2x - 5?

• Box method

• FOIL method

• Synthetic division

• Long division

What is the result of multiplying the binomials 3x + 2 and 2x - 5 using the FOIL method?

• 6x^2 - 11x - 10

• 6x^2 - 11x + 10

• 6x^2 + 11x - 10

• 6x^2 + 11x + 10

In the box method, what do you do after multiplying each term in the columns by each term in the rows?

• Subtract the results

• Combine like terms

• Add the results

• Divide the results

What is the first step in polynomial long division?

• Combine like terms

• Multiply the divisor by the first term of the dividend

• Subtract the divisor from the dividend

• Distribute the negative sign

What do you do after multiplying the divisor by the first term in polynomial long division?

• Combine like terms

• Divide the results

• Add the results

• Subtract the results

When can synthetic division be used?

• When the divisor has a leading coefficient other than 1

• When the dividend is a constant

• When the divisor is a trinomial

• When the divisor is a binomial with a leading coefficient of 1

In synthetic division, what operation is performed after multiplying the current term by the divisor?

• Subtract

• Divide

• Add

• Combine like terms